We analyze a semi-infinite one-dimensional random walk process with a biased motion that is incremental in one direction and long-range in the other. On a network with a fixed hierarchy of long-range jumps, we find with exact renormalization group calculations that there is a dynamical...

Based on a recently developed algorithm for the exploration of ground states in bond-diluted lattice spin glasses, we determine the scaling of defect energies with system size for Ising spin glasses at the bond percolation threshold pc. The results can be related by well-known scaling relations...